Graph Sin(2x+6): Is Parent Function the Best Option?

[barryj]

Homework Statement

Graph sin(2x+6)

Relevant Equations

period = 2pi/2, phase shift = 6/2

My question is when I start to graph sin (2x+6) I convert the expression to sin 2(x+3).
My thinking that by doing so I can easily see the period is 2pi/2 and there is a horizontal translation of 3. Some books state that starting with sin(2x+6) the period is 2pi/2 , the same as above, and that there is a phase shift of 6/2. I think it is better to start with a parent function of sin x, then apply horizontal compression and/or shift translations to get the correct graph.

Similarly for an absolute expression |2x-8| I always convert the expression to |2(x-4)| and apply translations.

Comments please?

 

[Office_Shredder]

You should do whatever makes sense to you.

Edit to add: Assuming it's also correct :)

 

[Mark44]

Homework Statement:: Graph sin(2x+6)
Relevant Equations:: period = 2pi/2, phase shift = 6/2

My question is when I start to graph sin (2x+6) I convert the expression to sin 2(x+3).
My thinking that by doing so I can easily see the period is 2pi/2 and there is a horizontal translation of 3. Some books state that starting with sin(2x+6) the period is 2pi/2 , the same as above, and that there is a phase shift of 6/2. I think it is better to start with a parent function of sin x, then apply horizontal compression and/or shift translations to get the correct graph.

Similarly for an absolute expression |2x-8| I always convert the expression to |2(x-4)| and apply translations.

Comments please?

Your strategy is the correct one. Look at compressions/expansions first, then reflections, and finally translations.
Starting from $y = \sin(x)$, the graph of $y = \sin(2x)$ is a compression by a factor of 2 toward the y-axis. Then $y = \sin(2(x + 3))$ is a translation of the compressed function by 3 units to the left. Similar idea for your absolute value function.

If you decompose your given function in the wrong order, you can sometimes wind up with the wrong result, so it's a good idea to check with a couple of points to make sure you've done things correctly.

 

[barryj]

At the high school here they are taught to calculate a phase shift of, in this example 6/2. Ultimately it is the same thing but when starting with 2x+6 the translation is not obvious. I guess our school is teaching "new math".

 

[Mark44]

At the high school here they are taught to calculate a phase shift of, in this example 6/2. Ultimately it is the same thing but when starting with 2x+6 the translation is not obvious. I guess our school is teaching "new math".

No, not "new math." To get the phase shift of 6/2, they are implicitly decomposing 2x + 6 into 2(x + 6/2) (I guess).

 

[barryj]

I was just kidding about the "new math". I guess I do not understand why they use the phase shift calculation rather than merely use what they already know about transformations.

 

[WWGD]

At the high school here they are taught to calculate a phase shift of, in this example 6/2. Ultimately it is the same thing but when starting with 2x+6 the translation is not obvious. I guess our school is teaching "new math".

Its a variable shift here; different shift for each value of x. If the shift was constant, then it would be , e.g., sin(x+3).